Problem: Solve for $x$ and $y$ using elimination. ${-x-2y = -13}$ ${x-5y = -8}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-7y = -21$ $\dfrac{-7y}{{-7}} = \dfrac{-21}{{-7}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {-x-2y = -13}\thinspace$ to find $x$ ${-x - 2}{(3)}{= -13}$ $-x-6 = -13$ $-x-6{+6} = -13{+6}$ $-x = -7$ $\dfrac{-x}{{-1}} = \dfrac{-7}{{-1}}$ ${x = 7}$ You can also plug ${y = 3}$ into $\thinspace {x-5y = -8}\thinspace$ and get the same answer for $x$ : ${x - 5}{(3)}{= -8}$ ${x = 7}$